The (b, c)-inverse in semigroups and rings with involution

2019/11/06 by Chen, Xiaofeng, Chen, Jianlong
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1911.02260

Abstract

In this paper, we first prove that if a is both left (b, c)-invertible and left (c, b)-invertible, then a is both (b, c)-invertible and (c, b)-invertible in a *-monoid, which generalized the recent result about the inverse along an element by Wang and Mosic, under the conditions (ab)* = ab and (ac)* = ac. In addition, we consider that ba is (c, b)- invertible, and at the same time ca is (b, c)-invertible under the same conditions, which extend the related results about Moore-Penrose inverses by Chen et al. to (b, c)-inverses. As applications, we obtain that under condition (a2)* = a2, a is an EP element if and only if a is one-sided core invertible if and only if a is group invertible.

Related

• A class of core inverses associated with Green's relations in semigroups
• The one-sided inverse along two elements in rings
• A new class of generalized inverses in semigroups and rings with involution
• The inverse along an element in rings
• Group, Moore-Penrose, core and dual core inverse in rings with involution